INCREASING THE ACCURACY OF FINANCIAL ACCOUNTING BY APPLYING MACHINE LEARNING FOR OPTION PRICING
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Introduction 6
Section 1. Options basics and problem statement 8
1.1. Options basics 8
1.2. Problem description 10
1.3. Research goals and expected results 13
Findings of section 1 15
Section 2. Analysis of existing approaches to option pricing 16
2.1. Parametric option pricing models 16
2.2. Non-parametric machine-learning methods for option pricing 22
2.3. Evaluation of option pricing models 24
Findings of section 2 27
Section 3. Methodology and data preparations 29
3.1. Methodology of the development of the ML-model for option pricing 29
3.2. Data description and transformations 31
3.3. Datasets preparation for model building 38
Findings of section 3 45
Section 4. Development of the ML-model for option pricing 46
4.1. Baseline model building 46
4.2. ML-models building 49
4.3. Final option pricing model selection and Greeks derivation 57
Findings of section 4 64
Conclusions 66
Project summary 66
Managerial implications 67
Limitations 68
Further research 69
Appendices 71
Appendix 1. Features RMSE input for implied volatility puts model 71
Appendix 2. Features RMSE input for implied volatility calls model 74
References 77
Section 1. Options basics and problem statement 8
1.1. Options basics 8
1.2. Problem description 10
1.3. Research goals and expected results 13
Findings of section 1 15
Section 2. Analysis of existing approaches to option pricing 16
2.1. Parametric option pricing models 16
2.2. Non-parametric machine-learning methods for option pricing 22
2.3. Evaluation of option pricing models 24
Findings of section 2 27
Section 3. Methodology and data preparations 29
3.1. Methodology of the development of the ML-model for option pricing 29
3.2. Data description and transformations 31
3.3. Datasets preparation for model building 38
Findings of section 3 45
Section 4. Development of the ML-model for option pricing 46
4.1. Baseline model building 46
4.2. ML-models building 49
4.3. Final option pricing model selection and Greeks derivation 57
Findings of section 4 64
Conclusions 66
Project summary 66
Managerial implications 67
Limitations 68
Further research 69
Appendices 71
Appendix 1. Features RMSE input for implied volatility puts model 71
Appendix 2. Features RMSE input for implied volatility calls model 74
References 77
Options are widely used by financial institutions and companies majorly as an insurance against the decrease or increase of the base asset price. When financial institutions or companies buy or sell such an insurance (an option contract) they need to estimate its fair price and risk sensitivity to various factors in order to understand whether such an operation is reasonable. Besides, any option-based operations are to be reported in the financial accounting, where they should be calculated based on the fair price of an option contract. The process of evaluation of this fair price is called option pricing and is widely used by financial institutions and other companies which use options in their operations.
Currently, financial institutions majorly rely on such conventional methods of option pricing as Black-Scholes model, Monte Carlo simulation, and others. The problem associated with the application of such methods is that they yield rather high estimation error, i.e. the price obtained with the help of such pricing models tends to be rather far from the actual value of a fair price. The reason for this is that such methods are parametric, the evaluation of the input parameters (e.g. implied volatility) is a rather complex and subjective task itself, and the quality of an option price estimation heavily depends on the quality of the estimation of the input parameters. Moreover, the conventionally used methods for option pricing rely on several assumptions which tend to be unsatisfied in real-world application, which also lowers the estimation quality. Although such methods for option pricing as Monte Carlo simulation or Binomial model prove to be more flexible and with fewer underlying assumptions in comparison with the Black-Scholes model, they need to be tuned for a particular option contract (e.g. to match the distribution of a randomly generated future base price with an observed distribution of the actual underlying security price in Monte Carlo model), which complicates their real-life application. Moreover, both Monte Carlo simulation and Binomial model are very computationally costly, which complicates their application for large datasets and real-time decision making, not to mention the difficulty of risk sensitivity analysis (so called option “Greeks”) based on these methods.
Transferring the described drawbacks of the conventional option pricing models into a business problem, first of all, the application of conventional models, compared to the modern approaches, increases the operational risk due to inaccuracy of the option price estimation, which in turn lowers the organization’s potential profit. Conventional models do not take in account such parameters as market capitalization or industry/sector of the economy, but it is empirically observed that using such factors can increase the accuracy of prediction. Secondly, the high computational complexity of the conventional models means the necessity to ensure respective computing resources, which increases the costs of supporting infrastructure. Moreover, long time 6
of computation makes the conventional methods inapplicable for real-time decision making, which also means delays in reaction to improve current risk exposure or to market opportunities and thus increases potential loses or decreases potential profits. Apart from that, the necessity to tune a parametric model to price a particular group of options increases both the maintenance costs and additional operational risk if such tuning is conducted manually.
Applying machine learning for option pricing along with availability of large historical datasets has a potential to solve the listed drawbacks of the conventional option pricing models. Therefore, in this project we aim to develop such a machine learning algorithm, which would outperform conventional option pricing models in terms of both prediction quality and computational time, being applicable for pricing options on any underlying asset.
In the first section of this paper, we provide basic theory about options, which is necessary to dive into context and understand the problem. Then we describe the existing problem with pricing options in financial accounting. Finally, based on the stated problem, we set the goal of the project, list research questions and tasks, and state the expected results.
In the second section, we analyze the existing approaches for option pricing proposed by different researchers. We start with analyzing such conventional option pricing models as Black- Scholes model, Binomial model, and Monte Carlo simulation, discussing their pros and cons. Then we observe the machine-learning based approaches for option pricing, highlighting particular algorithms used by different authors, model architectures, input parameter sets and other specifications. Finally, we list the metrics used to evaluate the quality of an option pricing model, describing how each metric is calculated, and when it should and when should not be applied.
In the third section, we describe the methodology of our research and data available for the analysis. We start with the high-level methodology outline, then we describe each data set used for the analysis, along with all the transformations we have done to the data and the applied cleaning procedure. Next, we split the data into training, validation, and test samples, and run feature importance analysis to select the meaningful model features.
In the fourth section, we develop a machine-learning approach for pricing options on any underlying asset. First, we run a Monte Carlo simulation as a baseline solution, to get the benchmark performance metrics, with which the following machine-learning models are to be compared. After that we test different machine-learning algorithms to solve the project problem, comparing their performance with each other and the baseline estimation. Finally, we choose the final algorithm and use it to derive the risk metrics (also called Greeks).
Currently, financial institutions majorly rely on such conventional methods of option pricing as Black-Scholes model, Monte Carlo simulation, and others. The problem associated with the application of such methods is that they yield rather high estimation error, i.e. the price obtained with the help of such pricing models tends to be rather far from the actual value of a fair price. The reason for this is that such methods are parametric, the evaluation of the input parameters (e.g. implied volatility) is a rather complex and subjective task itself, and the quality of an option price estimation heavily depends on the quality of the estimation of the input parameters. Moreover, the conventionally used methods for option pricing rely on several assumptions which tend to be unsatisfied in real-world application, which also lowers the estimation quality. Although such methods for option pricing as Monte Carlo simulation or Binomial model prove to be more flexible and with fewer underlying assumptions in comparison with the Black-Scholes model, they need to be tuned for a particular option contract (e.g. to match the distribution of a randomly generated future base price with an observed distribution of the actual underlying security price in Monte Carlo model), which complicates their real-life application. Moreover, both Monte Carlo simulation and Binomial model are very computationally costly, which complicates their application for large datasets and real-time decision making, not to mention the difficulty of risk sensitivity analysis (so called option “Greeks”) based on these methods.
Transferring the described drawbacks of the conventional option pricing models into a business problem, first of all, the application of conventional models, compared to the modern approaches, increases the operational risk due to inaccuracy of the option price estimation, which in turn lowers the organization’s potential profit. Conventional models do not take in account such parameters as market capitalization or industry/sector of the economy, but it is empirically observed that using such factors can increase the accuracy of prediction. Secondly, the high computational complexity of the conventional models means the necessity to ensure respective computing resources, which increases the costs of supporting infrastructure. Moreover, long time 6
of computation makes the conventional methods inapplicable for real-time decision making, which also means delays in reaction to improve current risk exposure or to market opportunities and thus increases potential loses or decreases potential profits. Apart from that, the necessity to tune a parametric model to price a particular group of options increases both the maintenance costs and additional operational risk if such tuning is conducted manually.
Applying machine learning for option pricing along with availability of large historical datasets has a potential to solve the listed drawbacks of the conventional option pricing models. Therefore, in this project we aim to develop such a machine learning algorithm, which would outperform conventional option pricing models in terms of both prediction quality and computational time, being applicable for pricing options on any underlying asset.
In the first section of this paper, we provide basic theory about options, which is necessary to dive into context and understand the problem. Then we describe the existing problem with pricing options in financial accounting. Finally, based on the stated problem, we set the goal of the project, list research questions and tasks, and state the expected results.
In the second section, we analyze the existing approaches for option pricing proposed by different researchers. We start with analyzing such conventional option pricing models as Black- Scholes model, Binomial model, and Monte Carlo simulation, discussing their pros and cons. Then we observe the machine-learning based approaches for option pricing, highlighting particular algorithms used by different authors, model architectures, input parameter sets and other specifications. Finally, we list the metrics used to evaluate the quality of an option pricing model, describing how each metric is calculated, and when it should and when should not be applied.
In the third section, we describe the methodology of our research and data available for the analysis. We start with the high-level methodology outline, then we describe each data set used for the analysis, along with all the transformations we have done to the data and the applied cleaning procedure. Next, we split the data into training, validation, and test samples, and run feature importance analysis to select the meaningful model features.
In the fourth section, we develop a machine-learning approach for pricing options on any underlying asset. First, we run a Monte Carlo simulation as a baseline solution, to get the benchmark performance metrics, with which the following machine-learning models are to be compared. After that we test different machine-learning algorithms to solve the project problem, comparing their performance with each other and the baseline estimation. Finally, we choose the final algorithm and use it to derive the risk metrics (also called Greeks).
In this paper, we have developed a machine learning algorithm for pricing options on any underlying asset.
First, we described the existing approach for option pricing applied in financial institutions and highlighted its drawbacks, which decrease the potential profit of a company. Based on the discovered problem, we set the goal of the project, listed research questions and tasks, and stated the expected results.
Second, we reviewed most commonly used conventional models for option pricing and discovered that Monte Carlo model proves to be one of the most flexible and precise ones, that is why we decided to use Monte Carlo method as a baseline solution to benchmark metrics of the designed machine-learning models. The major problem of Monte Carlo model is long computing time, thus we aimed to develop a ML-model which would work faster, yet yielding even better prediction quality than Monte Carlo method. Regarding particular machine learning algorithms to apply for option pricing, we have reviewed the best performing ones, according to the similar research, and decided to try the most promising ones, which include Random Forest, Gradient Boosting, and Neural Networks.
Third, based on the project goal, requirements, and similar research, we have designed a methodology for the development of the machine learning algorithm for option pricing. As has been proven in the similar research and double checked in our own empirical findings, the separate models for call and put options yield better prediction quality, comparing to the single model, this is why we decided to price call and put options separately. We have also decided to initially build models for predicting implied volatilities, since this factor needs to be included into the model for deriving the Vega coefficient. For each model we ran a separate feature selection analysis to get the features which help obtain the best predicting quality on a valid dataset. All in all, we ended up with developing four models: two models for estimating implied volatilities (for calls and puts) and two models for estimating option prices. Before modelling, we also cleaned the data to make the features homogeneous and the target variable reliable, thus to ensure model generalization and increase prediction quality.
Fourth, we started the modelling process with running Monte Carlo simulation to get a baseline solution and calculate benchmark metrics. Then we tried several machine learning algorithms and compared their performance with each other and with the baseline solution. Neural Network proved to be the best performing algorithm in terms of RMSE for call options, however for the out options LGBM performed slightly better. Nevertheless, the final choice was still for the Neural Network, since it is a differentiable machine-learning algorithm, which is more suitable for deriving Greek coefficients rather than a tree-based LGBM model, which might be insensitive to small changes of the input parameters. As for the final step of the modelling stage, we have built functions to calculate option Greeks and used them to get the estimations of the Greek coefficients for our data sample.
Managerial implications
The developed model can be easily integrated into the existing business processes and particular tools (Excel) currently used for option pricing in financial institutions. One possible implementation of such an integration is as follows. The model can be first packaged into the microservice, which in turn could be called in the Excel Macro. Then a user will need to enter the input parameters (or load them automatically, if to ensure connection to the database with up-to- date options data) and get an option price estimation.
The benefits of the implementation of the proposed ML-model for option pricing are as follows:
Autonomy and independence from the third-party solutions
Since all of the libraries used in the project are open-source, the developed solution for option pricing will be fully autonomous and robust to external actions. This is particularly valuable nowadays, when Russian banks have limited access to Bloomberg terminals and other software. The deployment of the self-developed tools will make the business processes more sustainable and mitigate the risk of losing the ability to perform particular activities.
Loss decrease due to the reduction of the reserves
When financial institutions buy or sell option contracts, they reserve the sum of money equal to the estimated option price plus the model risk. For example, if the model error (risk) equal to 20%, then a financial institution needs to reserve an estimated option price plus 20%. Implementing the proposed ML-solution for option pricing will decrease the model risk from 49% (if applying Monte Carlo method) to 11%, which yields 38% decrease of the necessary reserve sum, thus 38% loss decrease.
Increased profitability of speculative operations
Increased predicting time of the proposed model (268 times faster comparing to Monte Carlo method) makes it possible to quicker discover underestimated or overestimated traded option contracts and seize such opportunities to gain profit from buying or selling such options....
First, we described the existing approach for option pricing applied in financial institutions and highlighted its drawbacks, which decrease the potential profit of a company. Based on the discovered problem, we set the goal of the project, listed research questions and tasks, and stated the expected results.
Second, we reviewed most commonly used conventional models for option pricing and discovered that Monte Carlo model proves to be one of the most flexible and precise ones, that is why we decided to use Monte Carlo method as a baseline solution to benchmark metrics of the designed machine-learning models. The major problem of Monte Carlo model is long computing time, thus we aimed to develop a ML-model which would work faster, yet yielding even better prediction quality than Monte Carlo method. Regarding particular machine learning algorithms to apply for option pricing, we have reviewed the best performing ones, according to the similar research, and decided to try the most promising ones, which include Random Forest, Gradient Boosting, and Neural Networks.
Third, based on the project goal, requirements, and similar research, we have designed a methodology for the development of the machine learning algorithm for option pricing. As has been proven in the similar research and double checked in our own empirical findings, the separate models for call and put options yield better prediction quality, comparing to the single model, this is why we decided to price call and put options separately. We have also decided to initially build models for predicting implied volatilities, since this factor needs to be included into the model for deriving the Vega coefficient. For each model we ran a separate feature selection analysis to get the features which help obtain the best predicting quality on a valid dataset. All in all, we ended up with developing four models: two models for estimating implied volatilities (for calls and puts) and two models for estimating option prices. Before modelling, we also cleaned the data to make the features homogeneous and the target variable reliable, thus to ensure model generalization and increase prediction quality.
Fourth, we started the modelling process with running Monte Carlo simulation to get a baseline solution and calculate benchmark metrics. Then we tried several machine learning algorithms and compared their performance with each other and with the baseline solution. Neural Network proved to be the best performing algorithm in terms of RMSE for call options, however for the out options LGBM performed slightly better. Nevertheless, the final choice was still for the Neural Network, since it is a differentiable machine-learning algorithm, which is more suitable for deriving Greek coefficients rather than a tree-based LGBM model, which might be insensitive to small changes of the input parameters. As for the final step of the modelling stage, we have built functions to calculate option Greeks and used them to get the estimations of the Greek coefficients for our data sample.
Managerial implications
The developed model can be easily integrated into the existing business processes and particular tools (Excel) currently used for option pricing in financial institutions. One possible implementation of such an integration is as follows. The model can be first packaged into the microservice, which in turn could be called in the Excel Macro. Then a user will need to enter the input parameters (or load them automatically, if to ensure connection to the database with up-to- date options data) and get an option price estimation.
The benefits of the implementation of the proposed ML-model for option pricing are as follows:
Autonomy and independence from the third-party solutions
Since all of the libraries used in the project are open-source, the developed solution for option pricing will be fully autonomous and robust to external actions. This is particularly valuable nowadays, when Russian banks have limited access to Bloomberg terminals and other software. The deployment of the self-developed tools will make the business processes more sustainable and mitigate the risk of losing the ability to perform particular activities.
Loss decrease due to the reduction of the reserves
When financial institutions buy or sell option contracts, they reserve the sum of money equal to the estimated option price plus the model risk. For example, if the model error (risk) equal to 20%, then a financial institution needs to reserve an estimated option price plus 20%. Implementing the proposed ML-solution for option pricing will decrease the model risk from 49% (if applying Monte Carlo method) to 11%, which yields 38% decrease of the necessary reserve sum, thus 38% loss decrease.
Increased profitability of speculative operations
Increased predicting time of the proposed model (268 times faster comparing to Monte Carlo method) makes it possible to quicker discover underestimated or overestimated traded option contracts and seize such opportunities to gain profit from buying or selling such options....
Подобные работы
- INCREASING THE ACCURACY OF FINANCIAL ACCOUNTING BY APPLYING MACHINE LEARNING FOR OPTION PRICING
Магистерская диссертация, менеджмент. Язык работы: Английский. Цена: 4700 р. Год сдачи: 2022